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 Post subject: What is this polyhedron called?
PostPosted: Fri Mar 29, 2013 12:42 pm 
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I made this shape in my CAD software and want to know its official name. It has 56 sides (would that make it a pentacontahexahedron?) with 8 equilateral triangles, 24 isosceles triangles, and 24 rhombi. It also has 42 vertices and 96 edges. Is it a truncation or a kleetope of another shape? What is its dual shape? Any information on this polyhedron would help.
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File comment: Pentacontahexahedron?
mystery shape.jpg
mystery shape.jpg [ 186.28 KiB | Viewed 1054 times ]

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 Post subject: Re: What is this polyhedron called?
PostPosted: Sat Mar 30, 2013 1:07 pm 
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Alright, so after some more experimentation I managed to find its dual shape: 42 faces (6 squares, 12 rhombuses, and 24 irregular pentagons), 56 vertices, and 96 edges...
Attachment:
mystery shape dual.jpg
mystery shape dual.jpg [ 180.03 KiB | Viewed 984 times ]

...but I'm still confused. Does anyone know the names of either of these shapes? Also what is the edge-to-face equivalent? Like a Rhombic dodecahedron is to a cube.

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Last edited by benpuzzles on Sat Mar 30, 2013 2:18 pm, edited 1 time in total.

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 Post subject: Re: What is this polyhedron called?
PostPosted: Sat Mar 30, 2013 2:06 pm 
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I call it Fred. 8-)

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 Post subject: Re: What is this polyhedron called?
PostPosted: Sat Mar 30, 2013 7:31 pm 
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My guess is :
Edge-Truncated Rhombicuboctahedron

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 Post subject: Re: What is this polyhedron called?
PostPosted: Sat Mar 30, 2013 8:10 pm 
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JasonSmith wrote:
My guess is :
Edge-Truncated Rhombicuboctahedron

After entering this into the search engine, I got this image:

It's very close to the shape I described, but not quite the same, as the rhombi are not flat, but rather cut up into 2 triangles each. The website described it as a Rhombicuboctahedron L1/1V geodesic dome...
...interesting, I'll have to look more into this.

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 Post subject: Re: What is this polyhedron called?
PostPosted: Sun Mar 31, 2013 2:31 am 
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Hey Ben-
The 'kites' should be bent as you say. But the rhombuses are flat since they come directly from the truncation.
I think the image you found is a triangular tessellation for stability as a physical geodesic dome. And the rhombuses there do look flat to me.

I'm curious. How did you construct it? If it wasn't edge truncation of a rhombicuboctahedron, then I think that's very interesting!

Neat shape. I see a mixup cube in there.

In the geodesic tessellation you posted, are there only two triangle types? Pretty neat.

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 Post subject: Re: What is this polyhedron called?
PostPosted: Sun Mar 31, 2013 11:29 am 
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JasonSmith wrote:
I'm curious. How did you construct it? If it wasn't edge truncation of a rhombicuboctahedron, then I think that's very interesting!

I actually constructed it from a cuboctahedron. I transformed each square into a group of 4 rhombuses, and each triangle into a group of 4 triangles, using an arbitrary method.
JasonSmith wrote:
In the geodesic tessellation you posted, are there only two triangle types? Pretty neat.

Yes, that's right.

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